5D body in 5DII housing?

So from what I've been reading it sounds like the 5DII bodies typically don't fit into the 5D housings without modification because of the hotshoe (at least that is my understanding). Does it work the other way around? Can 5D bodies fit into 5DII? Presumably there would be a little extra headroom but other than that, is there anything else preventing the older body fitting into newer housings?

Sure it will fit but it will need a new baseplate and many of the buttons will not line up.

I am using a 5DII in a 5D housing.

Cheers

James